A portfolio manager would never prefer to make investment decision based on just one set of assumptions. Instead, he would evaluate the outcome of the selected strategy under various scenarios to determine what happens to total return when different sets of assumptions are used. This process of evaluating a strategy under several scenarios is called as scenario analysis. The various assumptions made for computing total return are assumptions regarding interest rates at the end of the investment horizon, spreads at the end of the horizon, and reinvestment rates over the investment horizon.
Controlling For Interest Rate Risk
When we assess two or more strategies, it is important to compare positions that have the same rupee duration. Duration is the change in the value of bond that will result from a 100 basis point change in yield. Let us consider two bonds P and Q. The price of bond P is 70 and has duration of 6%, and bond Y has a price of Rs.80 and duration of 5%. When the yield of bond P changes by 100 basis points, the value of the bond would change by Rs.4.2. For bond Q the value of the bond would change by Rs.4 for a change of 100 basis points. Now let us suppose that a portfolio manager has Rs.10,00,000 of par value of bond P. The market value of the portfolio is Rs.7,00,000. The rupee duration of the bonds for a change in 100 basis points in yield is equal to Rs.42,000. The manager decides to exchange the bonds for bond Q, but wants to maintain the same interest exposure on the new bonds that he intends to acquire. If he exchanges Rs.10,00,000 par value of bond P for Rs.10,00,000 par value of bond Q, the market value of bond Q will be equal to Rs.8,00,000. Then the new rupees duration would be Rs.40,000. Therefore to maintain same rupee duration the manager should purchase bond Q with market value equal to Rs.8,40,000. Then the rupees duration for the new portfolio will be Rs.42,000 (8,40,000 x 5%). For this, the manager should purchase Rs.10,50,000 of par value of bond Q.
The market value of bond Q needed to maintain same rupee duration as bond
P = Market value of bond Q = Rupee duration of P/duration of bond Q/100
Par value of the bond Y = Market value of bond Q/(Price of the bond Q/100)
Taking the data from the above example, we can see the working of the above two formulas as follows:
Duration of bond Q = 5
Rupee duration of bond P = Rs.42,000
Market value of bond Q = Rs.42,000/(5/100) = Rs.8,40,000
Par value of the bond Q = 8,40,000/(80/100) = Rs.10,50,000.
If a manager fails to adjust a trade based on some expected change in yield spread so as to hold the rupee duration the same, then the outcome of the trade will be affected by the change in the yield level and also by the expected change in the yield spread.